An effective way to couple FEM meshes and Peridynamics grids for the solution of static equilibrium problems

• Innovative strategy to couple Peridynamics (PD) grids with the Finite Element Method.
• No arbitrary choice or tuning of parameters or blending functions are required.
• No problem in the zone where the two approaches are merged is observed.
• The presented coupling method is a solution to the “surface problem” of PD.
• The new method can be easily implemented in commercial fem software.

Peridynamics is a continuum theory based on a non-local approach and capable of dealing with discontinuous displacement fields. The paper presents a technique to couple Peridynamic grids and finite element meshes to solve static equilibrium problems. The domain is divided in two zones: one discretized by the Peridynamic grid and the other where the Finite Element Method is applied. The coupling is achieved by considering that Peridynamics bonds act only on Peridynamic nodes, whereas finite elements apply forces only on finite element nodes. The proposed method was applied to study 1D and 2D examples. No problem in the zone of the structure where the two approaches are merged is observed. The results show that the coupling method is very effective and its simplicity suggests it can be easily introduced in commercial finite element codes.